Suppose there are two firms producing spring water which is homogeneous; that is, consumers don't particularly like one over the other if the prices charged by the two firms are the same. Suppose consumers' demand can be characterized by this linear demand Q = 40 2P and the marginal cost for both firms are the same, i.e., mc = 6. Both firms chose prices at which they sell their eater simultaneously,

a. Suppose both firms can produce as many units as possible to meet consumers' demand, i.e., no capacity constraint. Please derive both firms' demand functions given prices p1 and p2.

b. Suppose both firms can produce as many units as possible to meet consumers' demand, i.e., no capacity constraint. Please derive both firms' best response functions

c. What are the equilibrium prices, (p 1 , p 2 ).

d. If each firm has a capacity constraint q = 20, discuss whether a strategy profile (p1 = 6, p2 = 6) is a Nash Equilibrium or not?

e. If each firm has a capacity q = 10, meaning the maximal units that a firm can produce is 10, is strategy profile (p1 = 10, p2 = 10) a Nash Equilibrium or not?